## Linear Operators: Spectral theory |

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Page 888

Nelson Dunford, Jacob T. Schwartz. where a, 3 are arbitrary

where <f> is the void set. Here we have used the notations A Afi and A v B for the

intersection and union of two commuting projections A and B. We recall that

these ...

Nelson Dunford, Jacob T. Schwartz. where a, 3 are arbitrary

**spectral sets**andwhere <f> is the void set. Here we have used the notations A Afi and A v B for the

intersection and union of two commuting projections A and B. We recall that

these ...

Page 933

The

space, then von Neumann [3] defines a closed set S of the complex sphere to be

a

The

**spectral sets**of von Neumann. If T is a bounded linear operator in a Hilbertspace, then von Neumann [3] defines a closed set S of the complex sphere to be

a

**spectral set**of T if f(T) exists and f{T)\ 1 whenever / is a rational function such ...Page 993

the bounded measurable function (p has its

point m then, for some complex number a, q>(x) = <x[x, m] for almost all x in R.

Proof. In view of Lemma 11(d) it suffices to prove the theorem in the case m = 0.

the bounded measurable function (p has its

**spectral set**consisting of the singlepoint m then, for some complex number a, q>(x) = <x[x, m] for almost all x in R.

Proof. In view of Lemma 11(d) it suffices to prove the theorem in the case m = 0.

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### Contents

BAlgebras | 859 |

Commutative BAlgebras | 860 |

Commutative BAlgebras | 874 |

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Acad adjoint extension adjoint operator algebra Amer analytic B-algebra B*-algebra Banach spaces Borel set boundary conditions boundary values bounded operator closed closure coefficients complex numbers constant continuous function converges Corollary deficiency indices Definition denote dense differential equations Doklady Akad domain eigenfunctions eigenvalues element essential spectrum exists finite dimensional follows from Lemma follows from Theorem follows immediately formal differential operator formally self adjoint formula Fourier function g Haar measure Hence Hilbert space Hilbert-Schmidt operator hypothesis identity inequality integral interval kernel Lemma linear operator linearly independent mapping Math matrix measure Nauk SSSR N. S. neighborhood norm open set operators in Hilbert orthogonal orthonormal partial differential operator Plancherel's theorem positive Proc prove real axis real numbers representation satisfies second order Section sequence singular solution spectral set spectral theory square-integrable subspace Suppose symmetric operator topology transform unique unitary vanishes vector zero